The New Sudoku Players' Forum

[Yogi]

....31....2....4......8....26.4............81.........5..6..2....1..7...3......5.

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+---+---+---+
|...|.31|...|
|.2.|...|4..|
|...|.8.|...|
+---+---+---+
|26.|4..|...|
|...|...|.81|
|...|...|...|
+---+---+---+
|5..|6..|2..|
|..1|..7|...|
|3..|...|.5.|
+---+---+---+


[Hajime]

basics to

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   +-----------+-----------+--------------+ 
   | 8 a45  456|279  3   1 |e579 2679 2579| 
   | 1   2   79| 79  56  56| 4     3    8 | 
   |79   3   56|279  8   4 | 1   2679 2579| 
   +-----------+-----------+--------------+ 
   | 2   6   8 | 4   1   59|  3   79   579| 
   | 4 b579 579| 3   67  2 |  69   8    1 | 
   |79   1   3 | 8  567 569| 569  24   24 | 
   +-----------+-----------+--------------+ 
   | 5   8  479| 6   49  3 |  2    1   479| 
   | 6   49  1 | 5   2   7 |  8   49    3 | 
   | 3 c479  2 | 1   49  8 |d79    5    6 | 
   +--------------------------------------+ 


then

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AIC Type 2 [5 links] (5)-5-r1c2=(5-7)r5c2=7=r9c2-7-r9c7=7=r1c7 => (-5)r1c7
stte

Edit: added abcde into the grid

[RSW]

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 +------------+-------------+-----------------+
 | 8 b45  456 | 279 3   1   | a579  2679 2579 |
 | 1  2   79  | 79  56  56  |  4    3    8    |
 | 79 3   56  | 279 8   4   |  1    2679 2579 |
 +------------+-------------+-----------------+
 | 2  6   8   | 4   1   59  |  3    79   579  |
 | 4  579 579 | 3   67  2   |  6-9  8    1    |
 | 79 1   3   | 8   567 569 |  56-9 24   24   |
 +------------+-------------+-----------------+
 | 5  8   479 | 6   49  3   |  2    1    479  |
 | 6 b49  1   | 5   2   7   |  8    49   3    |
 | 3 b479 2   | 1   49  8   |ac79   5    6    |
 +------------+-------------+-----------------+


(9=75)r19c7 - (5=497)r189c2 - (7=9)r9c7 => -9r56c7; stte

[SteveG48]

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 *------------------------------------------------------------*
 |  8    e45   e456   | 279   3     1     |d579   2679  2579  |
 |  1     2     79    | 79    56    56    | 4     3     8     |
 |  79    3    f56    | 279   8     4     | 1     2679  2579  |
 *--------------------+-------------------+-------------------|
 |  2     6     8     | 4     1     59    | 3     79    579   |
 |  4     59-7 g579   | 3    a67    2     | 69    8     1     |
 |ag79    1     3     | 8     567  c569   |c569   24    24    |
 *--------------------+-------------------+-------------------|
 |  5     8     479   | 6     49    3     | 2     1     479   |
 |  6     49    1     | 5     2     7     | 8     49    3     |
 |  3     479   2     | 1     49    8     | 79    5     6     |
 *------------------------------------------------------------*


(7=69)r5c5,r6c1 - (6|9=5)r6c6 - r6c7 = r1c7 - r1c23 = r3c4 - (5=79)b4p67 => -7 r5c2 ; ste

[Cenoman]

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 +-------------------+--------------------+----------------------+
 |  8    45    456   |  279   3     1     |  579   2679   2579   |
 |  1    2     79    |  79    56    56    |  4     3      8      |
 |  79   3     56    |  279   8     4     |  1     2679   2579   |
 +-------------------+--------------------+----------------------+
 |  2    6     8     |  4     1     59    |  3     79     579    |
 |  4    579   579   |  3     67    2     |  69    8      1      |
 |  79   1     3     |  8     567   569   |  569   24     24     |
 +-------------------+--------------------+----------------------+
 |  5    8     479   |  6     49    3     |  2     1      479    |
 |  6    49    1     |  5     2     7     |  8     49     3      |
 |  3    479   2     |  1     49    8     |  79    5      6      |
 +-------------------+--------------------+----------------------+

(5=697)r569c7 - (7=495)r189c2 => -5 r1c7; ste

[P.O.]

basics:

Hidden Text: Show

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( n1r4c5   n2r9c3   n4r3c6   n6r8c1   n1r7c8   n1r9c4   n1r3c7
  n1r2c1   n1r6c2 )

intersections:
((((6 0) (2 5 2) (5 6 7 9)) ((6 0) (2 6 2) (5 6 9)))
 (((4 0) (6 8 6) (2 3 4 6 7 9)) ((4 0) (6 9 6) (2 3 4 5 6 7 9)))
 (((2 0) (6 8 6) (2 3 4 6 7 9)) ((2 0) (6 9 6) (2 3 4 5 6 7 9)))
 (((2 0) (5 6 5) (2 3 5 6 9)) ((2 0) (6 6 5) (3 5 6 8 9)))
 (((2 0) (1 4 2) (2 5 7 9)) ((2 0) (3 4 2) (2 5 7 9)))
 ( n3r8c9   n8r7c2   n3r2c8   n3r4c7   n8r2c9   n8r8c7   n4r5c1
   n3r3c2   n3r6c3   n8r1c1   n8r4c3   n8r9c6   n3r5c4   n3r7c6
   n8r6c4   n5r8c4   n2r5c6   n2r8c5 )
 (((9 0) (7 5 8) (4 9)) ((9 0) (9 5 8) (4 9)))
 (((9 0) (1 4 2) (2 7 9)) ((9 0) (2 4 2) (7 9)) ((9 0) (3 4 2) (2 7 9)))
 (((7 0) (5 5 5) (5 6 7)) ((7 0) (6 5 5) (5 6 7)))
 (((7 0) (4 8 6) (7 9)) ((7 0) (4 9 6) (5 7 9)))
 (((5 0) (5 2 4) (5 7 9)) ((5 0) (5 3 4) (5 7 9)))
 (((5 0) (2 5 2) (5 6)) ((5 0) (2 6 2) (5 6))))

PAIR BOX: ((2 3 1) (7 9)) ((3 1 1) (7 9)) 
(((1 2 1) (4 5 7 9)) ((1 3 1) (4 5 6 7 9)) ((3 3 1) (5 6 7 9)))

QUAD ROW: ((6 1 4) (7 9)) ((6 5 5) (5 6 7)) ((6 6 5) (5 6 9)) ((6 7 6) (5 6 9))
(((6 8 6) (2 4 6 9)) ((6 9 6) (2 4 5 6 9)))

intersections:
((((6 0) (1 8 3) (2 6 7 9)) ((6 0) (3 8 3) (2 6 7 9)))
 (((6 0) (5 7 6) (6 9)) ((6 0) (6 7 6) (5 6 9))) ( n6r9c9 ))


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8     45    456   279   3     1     579   2679  2579           
1     2     79    79    56    56    4     3     8             
79    3     56    279   8     4     1     2679  2579           
2     6     8     4     1     59    3     79    579           
4     579   579   3     67    2     69    8     1             
79    1     3     8     567   569   569   24    24             
5     8     479   6     49    3     2     1     479           
6     49    1     5     2     7     8     49    3             
3     479   2     1     49    8     79    5     6           

c2n5{r1 r5} - c2n7{r5 r9} - c7n7{r9 r1} => r1c7 <> 5
ste.


@Hajime: same as you this time again, but i only count 3 links and not 5 same as the previous time
in fact for me it is a condensed notation as a chain of an OR relationship between two terms, one of the terms has 1 link the other term has 3 links:

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Elimination: ((((1 7 3) (5 7 9))) (5))      r1c7<>5

((5 0) (1 2 1) (4 5))                       r1c2=5

((5 0) (5 2 4) (5 7 9))                     r5c2=5
((7 1 10) (9 2 7) (4 7 9))        r5c2<>7 - r9c2=7
((7 2 1) (1 7 3) (5 7 9))         r9c7<>7 - r1c7=7


[Hajime]

@Hajime: same as you this time again, but i only count 3 links and not 5 same as the previous time
in fact for me it is a condensed notation as a chain of an OR relationship between two terms, one of the terms has 1 link the other term has 3 links:

AIC:
A. strong link, if r1c2 is not a 5 then r5c2 is a 5
B. weak link, if r5c2 is a 5 it can not be a 7
C. strong link, if r5c2 is not a 7 then r9c2 must be a 7
D. weak link, if r9c2 is a 7 then r9c7 is not a 7
E. strong link, if r9c7 is not a 7 then r1c7 must be a 7
5 links

And of course: If r1c2=5 then r1c7 is not 5

Either way: r1c7 can never be a 5

So 5 links, but my Eureka notation is maybe not optimal.

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AIC Type 2 [5 links] (5)-5-r1c2=(5-7)r5c2=7=r9c2-7-r9c7=7=r1c7 => (-5)r1c7

I am open for improvements.

[P.O.]

i see, i don't have strong or weak links i only have links, what set contexts on the resolution state
so i guess you don't have the following kind of chain as to get the third link it uses the context set by the two previous links:

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r1c2{n5 n4} - r8c2{n4 n9} - r9c2{n49 n7} - c7n7{r9 r1} => r1c7 <> 5
ste.


[Hajime]

i see, i don't have strong or weak links i only have links, what set contexts on the resolution state
so i guess you don't have the following kind of chain as to get the third link it uses the context set by the two previous links:

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r1c2{n5 n4} - r8c2{n4 n9} - r9c2{n49 n7} - c7n7{r9 r1} => r1c7 <> 5
ste.


You assumed correct. I would not find this last chain.
(I am busy with context in SiSeSuSo, to avoid too large AIC search trees)

BTW in your chains you do have strong/weak links:
in {a b} there is a strong link between a and b
and } - { is a weak link.

[P.O.]

i think i understand what strong and weak links mean, i wanted to say that i don't conceptualize a chain in this way
that said, i'm not criticizing what you're doing, it works, which is enough to validate your approach

[Cenoman]

Maybe should I refrain myself from interfering...

AIC Type 2 [5 links] (5)-5-r1c2=(5-7)r5c2=7=r9c2-7-r9c7=7=r1c7 => (-5)r1c7
stte

and in another post:

So 5 links, but my Eureka notation is maybe not optimal.

In Eureka notation, I'd write:
(5)r1c2 = (5-7)r5c2 = r9c2 - r9c7 = (7)r1c7 => -5 r1c7

Some players in this forum would write the chain even more simply: 5r1c2 = (5-7)r5c2 = r9c2 - r9c7 = 7r1c7 (w/o brackets around single digits).
The result of the chain can also be written r1c7 <> 5 (Original Eureka specification)

In any case, no need to redundantly focus on the linking digit at each node.
As regards the link count, the most frequent use is to give the length of an AIC by its count of Strong Links. As an AIC has a strong link at both its endpoints, it has exactly n-1 weak links (n being its strong link count). As an echo to a recent discussion here (previous Yogi's puzzle), your chain has a length 3, and therefore is a Wing, L2-Wing according to my naming.
Hope this helps.

[Hajime]

P.O. and Cenoman, thank you both, just learned a lot.
I took the AIC-notation from Hodoku, but that is not the same as Eureka.
Sudocue (from Eureka) uses r1c7<>5, but I was stubborn and wanted all the candidates to be in ().
I did not know that the length of an AIC is counted in strong links only, that makes sense.
So my 5-link AIC will become a 3-link AIC, which P.O. already stated.
And I will omit unnecessary () and leave the Hodoku notation.
I have to check if I can find all the {Y, H, W, S, M, L}-Wing methods.